We study the generalization of the spin-boson model to spins greater than one-half in the strong-coupling regime. This model applies to dissipative large spins as well as to ensembles of identical two-state systems coupled to a common environment. Using a combination of polaron transformations and master equations, we find nonexponential spin relaxation towards one of two possible equilibrium states. For Ohmic dissipation the relaxation is approximately logarithmic in time.

We consider the optimal cloning of quantum coherent states with single-clone and joint fidelity as figures of merit. While the latter is maximized by a Gaussian cloner, the former is not: the optimal single-clone fidelity for a symmetric 1-to-2 cloner is 0.6826, compared to $2/3$ in a Gaussian setting. This cloner can be realized with an optical parametric amplifier and certain non-Gaussian bimodal states. Finally, we show that the single-clone fidelity of the optimal $1\mathrm{\text{-to-}}\infty$ cloner is $1/2$. It is achieved by a Gaussian scheme and cannot be surpassed even with supplemental bound entangled states.

An optical speckle potential is used to investigate the static and dynamic properties of a Bose-Einstein condensate in the presence of disorder. With small levels of disorder, stripes are observed in the expanded density profile and strong damping of dipole and quadrupole oscillations is seen. Uncorrelated frequency shifts of the two modes are measured and are explained using a sum-rules approach and by the numerical solution of the Gross-Pitaevskii equation.

Using a combination of statistical mechanics and finite-element interpolation, we develop a coarse-grained (CG) alternative to molecular dynamics (MD) for crystalline solids at constant temperature. The new approach is significantly more efficient than MD and generalizes earlier work on the quasicontinuum method. The method is validated by recovering equilibrium properties of single crystal Ni as a function of temperature. CG dynamical simulations of nanoindentation reveal a strong dependence on temperature of the critical stress to nucleate dislocations under the indenter.

We study the molecular behavior of two atoms interacting near a Feshbach resonance in the presence of a 1D periodic potential. The critical value of the scattering length needed to produce a molecule and the binding energy at resonance are calculated as a function of the intensity of the periodic potential. Because of the nonseparability of the center of mass and relative motion, the binding energy depends on the quasimomentum of the molecule. This has dramatic consequences on the molecular tunneling properties, which become strongly dependent on the scattering length.

We study low temperature properties of a spinless interacting Fermi gas in the trimerized kagomé lattice. The case of two fermions per trimer is described by a quantum spin $1/2$ model on the triangular lattice with couplings depending on the bond directions. Using exact diagonalizations we show that the system exhibits nonstandard properties of a quantum spin-liquid crystal, combining a planar antiferromagnetic order with an exceptionally large number of low-energy excitations.

We derive the optimal universal broadcasting for mixed states of qubits. We show that the no-broadcasting theorem cannot be generalized to more than a single input copy. Moreover, for four or more input copies it is even possible to purify the input states while broadcasting. We name such purifying broadcasting superbroadcasting.

We study the phase structure of a dilute two-component Fermi system with attractive interactions as a function of the coupling and a finite number asymmetry or polarization. In weak coupling, a number asymmetry results in phase separation. A mixed phase containing symmetric superfluid matter and an asymmetric normal phase is favored. For strong coupling we show that the stress on the superfluid phase to accommodate a number asymmetry increases. Near the infinite-scattering length, we calculate the single-particle excitation spectrum and the ground-state energy. A picture of weakly interacting quasiparticles emerges for modest polarizations. In this regime a homogeneous phase with a finite population of quasiparticle states characterized by a gapless spectrum is favored over the phase separated state. These states may be realized in cold atom experiments.

We demonstrate experimentally a robust quantum memory using a magnetic-field-independent hyperfine transition in atomic ion qubits at a magnetic field . We observe that the single physical qubit memory coherence time is greater than 10 s, an improvement of approximately 5 orders of magnitude from previous experiments with . We also observe long coherence times of decoherence-free subspace logical qubits comprising two entangled physical qubits and discuss the merits of each type of qubit.

We present a cluster algorithm for resistively shunted Josephson junctions or similar physical systems, which dramatically improves sampling efficiency, and apply it to the superconductor-to-metal transition in a single junction. Measuring the temperature dependence of the zero bias resistance, we confirm that the critical point does not depend on the strength of the Josephson coupling. However, we find that the correlation exponents vary continuously along the phase boundary, indicating that the Schmid-Bulgadaev transition is a line of fixed points.

In a Rabi oscillation experiment with a superconducting qubit we show that a visibility in the qubit excited state population of more than 95% can be attained. We perform a dispersive measurement of the qubit state by coupling the qubit nonresonantly to a transmission line resonator and probing the resonator transmission spectrum. The measurement process is well characterized and quantitatively understood. In a measurement of Ramsey fringes, the qubit coherence time is larger than 500 ns.

We propose a conjugate application of the Bargmann representation of quantum mechanics. Applying the Maslov method to the semiclassical connection formula between the two representations, we derive a uniform semiclassical approximation for the coherent-state propagator which is finite at phase space caustics.

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal Stiefel $U(N)$ bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this holonomy captures the inherent geometric feature of the state evolution that may not be cyclic. Moreover, a rigorous theory of geometric phase in the evolution of the eigenspace of an adiabatic action operator is also formulated, with the corresponding holonomy being elaborated by a pullback $U(N)$ bundle.

A method of solving the Schrödinger equation in an analytically expanded form reported previously is extended to the relativistic case and a general method of exactly solving the Dirac-Coulomb equation has been proposed for atoms and molecules. Some problems characteristic of the relativistic case are discussed. Test applications to the hydrogenlike, heliumlike atoms are satisfactory, implying a high potentiality of the proposed method also for the relativistic case.

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle-hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible kinks are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator.

Given a black box for $f$, a smooth real scalar function of $d$ real variables, one wants to estimate $\nabla f$ at a given point with $n$ bits of precision. On a classical computer this requires a minimum of $d+1$ black box queries, whereas on a quantum computer it requires only one query regardless of $d$. The number of bits of precision to which $f$ must be evaluated matches the classical requirement in the limit of large $n$.

We investigate the stability properties of breather solitons in a three-dimensional Bose-Einstein condensate with Feshbach resonance management of the scattering length and confined only by a one-dimensional optical lattice. We compare regions of stability in parameter space obtained from a fully 3D analysis with those from a quasi-two-dimensional treatment. For moderate confinement we discover a new island of stability in the 3D case, not present in the quasi-2D treatment. Stable solutions from this region have nontrivial dynamics in the lattice direction; hence, they describe fully 3D breather solitons. We demonstrate these solutions in direct numerical simulations and outline a possible way of creating robust 3D solitons in experiments in a Bose-Einstein condensate in a one-dimensional lattice. We point out other possible applications.

Polarization-dependent phase-contrast imaging is used to resolve the spatial magnetization profile of an optically trapped ultracold gas. This probe is applied to Larmor precession of degenerate and nondegenerate spin-1 ${}^{87}\mathrm{Rb}$ gases. Transverse magnetization of the Bose-Einstein condensate persists for the condensate lifetime, with a spatial response to magnetic field inhomogeneities consistent with a mean-field model of interactions. In comparison, the magnetization of the noncondensed gas decoheres rapidly. Rotational symmetry implies that the Larmor frequency of a spinor condensate be density independent, and thus suitable for precise magnetometry with high spatial resolution.

We introduce a novel semiclassical approach to the Lipkin model. In this way the well-known phase transition arising at the critical value of the coupling is intuitively understood. New results—showing for strong couplings the existence of a threshold energy which separates deformed from undeformed states as well as the divergence of the density of states at the threshold energy—are explained straightforwardly and in quantitative terms by the appearance of a double well structure in a classical system corresponding to the Lipkin model. Previously unnoticed features of the eigenstates near the threshold energy are also predicted and found to hold.

We describe a new experimental approach to probabilistic atom-photon (signal) entanglement. Two qubit states are encoded as orthogonal collective spin excitations of an unpolarized atomic ensemble. After a programmable delay, the atomic excitation is converted into a photon (idler). Polarization states of both the signal and the idler are recorded and are found to be in violation of the Bell inequality. Atomic coherence times exceeding several microseconds are achieved by switching off all the trapping fields—including the quadrupole magnetic field of the magneto-optical trap—and zeroing out the residual ambient magnetic field.